KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 36 of 120

Marks: +1, -0

A rectangular region of dimensions w × l (w << l) has a constant magnetic field into the plane of the paper as shown. On one side the region is bounded by a screen. On the other side positive ions of mass m and charge q are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference V < 0, and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen ?

Ions with $q > {2 | v | m}/ {B^2 w^2}$ will hit the screen.
Ions with $q < {2 | v | m}/ {B^2 w^2}$ will hit the screen.
All ions will hit the screen.
Only ions with $q = {2 | v | m}/ {B^2 w^2}$ will hit the screen.

Validate

Solution:

Ions will hit if r > w.

w = q∆V

1/2 mv^ 2 = qV

v=√{{2qV}/m}

{mv^ 2 }/r=qvB

⇒

r={mv}/{qB}=m/{qB}√{{2qV}/m}

r=1/B√ {{2mV}/q}

1/B√{{2mV}/q}>w

{2qV}/m >w^2B^2

⇒

q< {2mV}/{w^2B^2 }

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